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\begin{equation}
\begin{aligned}
&amp; x_1^{\prime}=F_1(t, x_1, \cdots, x_n)=p_{11}(t) x_1+p_{12}(t) x_2+\cdots+p_{1n}(t) x_n+g_1(t),\\
&amp; x_2^{\prime}=F_2(t, x_1, \cdots, x_n)=p_{21}(t) x_1+p_{22}(t) x_2+\cdots+p_{2n}(t) x_n+g_2(t),\\
&amp;\cdots,\\
&amp;x_n^{\prime}=F_n(t, x_1, \cdots, x_n)=p_{n1}(t) x_1+p_{n2}(t) x_2+\cdots+p_{nn}(t) x_n+g_n(t).
\end{aligned}\tag{6.1.2}
\end{equation}
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